Advanced Geometry : Advanced Geometry

Study concepts, example questions & explanations for Advanced Geometry

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Example Questions

Example Question #191 : Advanced Geometry

Which graph correctly represents the position of the point at ?

Possible Answers:

Coordinate_pair_3

Coordinate_pair_4

Coordinate_pair_5

Coordinate_pair_2

Correct answer:

Coordinate_pair_3

Explanation:

Coordinate points are given x-coordinate first, y-coordinate second.  The correct representation plots the point one unit to the left of the origin on the x-axis and four units up from the origin on the y-axis.

Example Question #13 : How To Graph An Ordered Pair

Coordinate_pair_6

Which of the following correctly identifies Points A and B, in that order, on the line?

Possible Answers:

Correct answer:

Explanation:

Coordinate points are given x-coordinate first, y-coordinate second.

(-2, 1), (2, 4) is correct because it list the coordinates of each point in the correct order.

(1, -2), (4, 2) is incorrect because it lists the coordinates of each point in the incorrect order.

(2, 4), (-2, 1) is incorrect because, while it lists the coordinates of each point correctly, it misidentifies the points.

(4, 2), (1, -2) is incorrect because it both lists the coordinates of each point in the incorrect order and misidentifies the points.

Example Question #102 : Graphing

Which quadrants can include the point   if nonzero numbers  and  have the same sign?

Possible Answers:

Either Quadrant I or Quadrant II

Either Quadrant II or Quadrant IV

Either Quadrant II or Quadrant III

Either Quadrant I or Quadrant III

Either Quadrant I or Quadrant IV

Correct answer:

Either Quadrant I or Quadrant IV

Explanation:

If  and  have the same sign, then , and the point has a positive -coordinate. The sign of  is the same as the common sign of  and . Therefore, only the -coordinate restricts the possibilities.

The points witn positive -coordinates are in Quadrant I and Quadrant IV.

Example Question #102 : Coordinate Geometry

Which quadrant or axis can include the point ?

Possible Answers:

Quadrant IV

The -axis

Quadrant III

Quadrant II

Quadrant I

Correct answer:

Quadrant I

Explanation:

The ordered pair  consists of a positive -coordinate and a positive -coordinate. The only quadrant that consists entirely of positive - and -coordinates is Quadrant I. 

Example Question #1031 : Gmat Quantitative Reasoning

Which quadrant or axis contains the point ?

Possible Answers:

The -axis

Quadrant III

Quadrant II

The -axis

Quadrant I

Correct answer:

The -axis

Explanation:

The ordered pair  consists of a positive -coordinate and a -coordinate of . The only part of the coordinate plane on which all points have a zero -coordinate is the -axis. 

Example Question #22 : How To Graph An Ordered Pair

Which of the following ordered pairs is in Quadrant III?

Possible Answers:

Correct answer:

Explanation:

By definition, only Quadrant III contains ordered pairs that have both negative - and -coordinates. 

Example Question #103 : Coordinate Geometry

Which quadrant or axis includes the point ?

Possible Answers:

Quadrant II

Quadrant I

The -axis

Quadrant IV

Quadrant III

Correct answer:

Quadrant II

Explanation:

The ordered pair  has a negative -coordinate and a positive -coordinate. By definition, all ordered pairs with negative -coordinates and a positive -coordinates exist in Quadrant II.

Example Question #108 : Graphing

Which quadrant or axis includes the point ?

Possible Answers:

Quadrant III

The -axis

The -axis

Quadrant I

Quadrant II

Correct answer:

The -axis

Explanation:

The ordered pair  has a zero -coordinate and a nonzero -coordinate. By definition, all ordered pairs with zero -coordinates and nonzero -coordinates is on the -axis.

Example Question #51 : Graphing

Which of the following ordered pairs is in Quadrant I?

Possible Answers:

None of these coordinates

Correct answer:

Explanation:

 By definition, all ordered pairs with positive -coordinates and positive -coordinates are in Quadrant I. Therefore, the only ordered pair in this quadrant is .

Example Question #105 : Coordinate Geometry

In which quadrant is the point ?

Possible Answers:

Quadrant II

Quadrant I

Quadrant III

Quadrant IV

Correct answer:

Quadrant II

Explanation:

The quadrants are numbered as follows:

Quadrants

The point (-2,3) has a negative x coordinate, so the point is on the left side of the y-axis, and a positive y-coordinate, so the point is above the x-axis.

That places it in quadrant II.

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